An outline of shaping work of a stepped shaft by means of a cross-rolling machine is shown in FIGS. 1 and 2. FIG. 1(a) shows a cross-rolling process by means of rolling dies, while FIG. 1(b) shows an operating state where flat dies are employed. In FIG. 1(a), a raw material rod 03 is interposed between rolls 01, 01, so that as the rolls 01, 01 rotate in the same direction the raw material rod can be pinched to be shaped into a desired form by means of dies 02, 02 mounted on the rolls 01, 01, respectively.
In FIG. 1(b) also, the operation principle is the same as that explained with reference to FIG. 1(a), and the only difference exists in that the dies are developed on flat planes.
FIGS. 2(a), 2(b) and 2(c) illustrate the steps of shaping a raw material rod upon roll-forming a raw material rod having a diameter d.sub.o until the diameter of its center portion is reduced to d as the aforementioned dies rotate or advance.
At II-a in FIG. 2(a) is shown a developed plan view of a roll-forming die, and at II-b on the left side of the same figure is shown a cross-section view of the final part of the same die taken at right angles to the direction of advance. In addition, at II-c in FIG. 2(b) is shown a longitudinal cross-section view of the same die, and FIG. 2(c) shows at III-a to III-e the roll-formed states of the raw material rod at various portions of the die. For instance, at III-c is shown the state of the raw material rod when it is positioned along line Z--Z on the die while being roll-formed. In these figures, reference characters .alpha. and .beta. designate a wedge angle and an advance angle, respectively, of the die, and reference character h designates a height of the die, as known in the art.
A cylindrical raw material rod is successively shaped and finished into a final product while the dies are advanced and roll-forming proceeds as shown at III-a to III-e in FIG. 2(c).
In addition, as well-known in the art, a die basically consists of a bite portion A, a depression spreading portion B and a finishing portion C as shown at II-a in FIG. 2(a), and these portions, respectively, achieve the rolls of biting into a rawmaterial rod up to a predetermined diameter d of a product, further spreading a depression of the raw material rod along a predetermined cylindrical surface or a predetermined contour, and smoothly finishing the product so as to have a desired final product shape. In FIG. 2, at III-b is shown the shape of the roll-formed article at the end point of the bite portion, that is, at the start point of the depression spreading portion, at III-d is shown the shape of the roll-formed article at the end point of the depression portion, that is, at the start point of the finishing parallel portion, and at III-e is shown the shape of the final product. The cross-section shapes of the die at the cross-sections corresponding to the roll-formed articles shown at III-d and III-e, respectively, are the same, and the heights h of the die at the cross-sections corresponding to the roll-formed articles shown at III-b, III-c, III-d and III-e, respectively, are kept constant.
However, as well-known in the art, if the ratio d/d.sub.o of the final diameter d of the product to the diameter d.sub.o of the raw material rod or the maximum diameter d.sub.o of the product as shown in FIG. 2(c) is too small, that is, if a diameter reduction factor d.sub.o /d is too large, then during the roll-forming work, a piercing phenomenon due to Mannesmann effects would arise at the center of the shaft portion, constriction (notching) would occur at the shaft portion of the product, or in the worst case the product would be torn off. Therefore, roll-forming of a stepped shaft having a large diameter reduction faction was impossible by means of the conventional dies.
As described above, the diameter reduction factor that can be imposed to an article by means of the conventional dies for use in a cross-rolling machine was limited, and the limit value of the diameter reduction factor would vary depending upon the wedge angle .alpha. and the advance angle .beta. as shown in FIG. 2, but normally it was substantially equal to 75%. Accordingly, shaping of a stepped shaft by employing the cross-rolling process was limited with respect to the diameter reduction factor, and there were many unpracticable cases, in which a great cost reduction could be expected if the cross-rolling process were to be applicable.
In FIGS. 3(a) and 3(b) is shown the relation between a rod being roll-formed and dies at any arbitrary position within the depression spreading portion B as shown in FIG. 2(a), and in these figure, reference numerals 02a and 03a designate cross-sections of the dies and the rod being roll-formed, respectively, taken along the axis of the rod. The cause of the generation of constriction (notching) in the case of the conventional dies for cross-rolling machines, was a component of force P.sub.Y in the axial direction of the rod being roll-formed of a roll-forming force P exerted upon the rod 03 being roll-formed via the pinching surfaces 04 during the roll-forming process as shown in FIG. 3(a), and the rod 03 being roll-formed has its cylindrical portion having a diameter d and placed between the unpinching top surfaces 05, 05 of the dies subjected to an axial tension 2P.sub.Y via the pinching surfaces 04, 04 of the dies on both the upper and lower sides, as shown in the figure. In this case, assuming that the diameter d.sub.o of the raw material rod or the maximum diameter d.sub.o of the product is kept constant and the wedge angle .alpha. as well as the advance angle .beta. shown in FIG. 2 are also kept constant, then the length of the pinching surface 04 as measured along the direction inclined by the wedge angle .alpha. with respect to the axis is increased as the minimum diameter d of the product is reduced, and thus the roll-forming force is increased, so that the axial tension 2P.sub.Y is also enhanced. In addition, as the minimum diameter d is reduced, the circular cross-section area .pi./4d.sup.2 of this portion taken ar right angles to the axis is also reduced, so that the tensile stress 2P.sub.Y /.pi./4d.sup.2 is further increased, and if this tensile stress value exceeds a predetermined value, then constriction would arise in the material similarly to the case of tension test.